z Score Calculator

Single Value Sample Mean

Your Value (x)

The individual data point you want to standardize.

Population Mean (μ)

Population Standard Deviation (σ)

About This Tool

What Is a Z-Score?

A z-score tells you how many standard deviations a value sits above or below the mean. A z-score of 0 means the value equals the mean; positive means above, negative means below.

When to Use It

Comparing a value to a known population mean and standard deviation
Standardizing scores so they can be compared across different scales
Finding what percentage of a population falls above or below a given value

The Formula

\[ z = \frac{x - \mu}{\sigma} \quad \text{(single value)} \qquad z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}} \quad \text{(sample mean)} \]

Worked Example

A student scores 85 on a test with a class mean of 70 and standard deviation of 10.

\( z = (85-70)/10 = 1.5 \)
The score is 1.5 standard deviations above the mean.
That corresponds to about the 93rd percentile — the student scored higher than roughly 93% of the class.

Your Results

Z-Score

Percentile

% Below

% Above

What This Means

Where It Falls on the Curve

Perfect for students, researchers, and professionals looking to build real statistical skills.

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